The length of k in the triangle KLM is 6.5 inches.
How to find the side length of a triangle?
The triangle KLM has the length l = 2.4 inches, and ∠K = 159 degrees. The length of k in the triangle to the nearest tenth of an inches can be calculated as follows;
Using the cosine rule for triangle,
k² = m² + l² - 2ml cos K
Therefore,
k² = 4.2² + 2.4² - 2 × 4.2 × 2.4 cos 159°
k² = 17.64 + 5.76 - 20.16 × -0.93358042649
k² = 23.4 + 18.8209813982
k² = 42.22
square root both sides
k = √42.22
k = 6.4976918979
Therefore,
The value of k in the triangle KLM is 6.5 inches.